Authors:

Christian Guill(TU Darmstadt, Institute of Condensed Matter Physics)

Barbara Drossel(TU Darmstadt, Institute of Condensed Matter Physics)

The number of spawning sockeye salmon that return to their native
streams in the Fraser river basin exhibit striking four-year
oscillations, the dimension of which being no less notable than
the widely known cycles of lynx and snowshoe hare in Canada. The
period of the oscillation corresponds to the dominant generation
time of these fish, and the phase differs between different
stocks. Various not fully convincing explanations have been
attempted, ascribing this phenomenon to transient effects, to
stochastic influences, to depensatory predation, or to genetic
effects.
We show that these oscillations can be explained as a stable
dynamical attractor of the population dynamics, resulting from a
strong resonance near a Neimark Sacker bifurcation. This explains
not only the long-term persistence of these oscillations, but
also reproduces correctly the sequence of two strong years
followed by two weak years. Furthermore, it explains the
observations that the oscillations occur only in oligotrophic
lakes, and that they do not occur in salmon species that have a
longer generation time.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.A27.15